Optimal. Leaf size=27 \[ \frac{3}{10} e^{-t} \sin (3 t)-\frac{1}{10} e^{-t} \cos (3 t) \]
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Rubi [A] time = 0.0111672, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1, Rules used = {4433} \[ \frac{3}{10} e^{-t} \sin (3 t)-\frac{1}{10} e^{-t} \cos (3 t) \]
Antiderivative was successfully verified.
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Rule 4433
Rubi steps
\begin{align*} \int e^{-t} \cos (3 t) \, dt &=-\frac{1}{10} e^{-t} \cos (3 t)+\frac{3}{10} e^{-t} \sin (3 t)\\ \end{align*}
Mathematica [A] time = 0.0269654, size = 20, normalized size = 0.74 \[ -\frac{1}{10} e^{-t} (\cos (3 t)-3 \sin (3 t)) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 22, normalized size = 0.8 \begin{align*} -{\frac{{{\rm e}^{-t}}\cos \left ( 3\,t \right ) }{10}}+{\frac{3\,{{\rm e}^{-t}}\sin \left ( 3\,t \right ) }{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.936622, size = 23, normalized size = 0.85 \begin{align*} -\frac{1}{10} \,{\left (\cos \left (3 \, t\right ) - 3 \, \sin \left (3 \, t\right )\right )} e^{\left (-t\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.87896, size = 62, normalized size = 2.3 \begin{align*} -\frac{1}{10} \, \cos \left (3 \, t\right ) e^{\left (-t\right )} + \frac{3}{10} \, e^{\left (-t\right )} \sin \left (3 \, t\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.458049, size = 20, normalized size = 0.74 \begin{align*} \frac{3 e^{- t} \sin{\left (3 t \right )}}{10} - \frac{e^{- t} \cos{\left (3 t \right )}}{10} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05177, size = 23, normalized size = 0.85 \begin{align*} -\frac{1}{10} \,{\left (\cos \left (3 \, t\right ) - 3 \, \sin \left (3 \, t\right )\right )} e^{\left (-t\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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